Optimal minimum distance under arbitrary support constraints on parity-check matrices is derived and achievable over large fields, but not always via generalized Reed-Solomon subcodes, as shown by a K_{6,6} incidence counterexample.
Optimum linear codes with support-constrained generator matrices over small fields
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On Codes with Support-Constrained Parity Checks
Optimal minimum distance under arbitrary support constraints on parity-check matrices is derived and achievable over large fields, but not always via generalized Reed-Solomon subcodes, as shown by a K_{6,6} incidence counterexample.